YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D) -> stop(A,B,C,D) [0 >= A && B = C && D = A] (?,1) 1. start(A,B,C,D) -> lbl6(A,B,C,D) [A >= 1 && 0 >= C && B = C && D = A] (?,1) 2. start(A,B,C,D) -> cut(A,B,C,D) [A >= 1 && D = A && B = A && C = A] (?,1) 3. start(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [A >= 1 && C >= 1 + A && B = C && D = A] (?,1) 4. start(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [A >= 1 + C && C >= 1 && B = C && D = A] (?,1) 5. lbl6(A,B,C,D) -> stop(A,B,C,D) [A >= 1 && 0 >= C && D = A && B = C] (?,1) 6. lbl101(A,B,C,D) -> cut(A,B,C,D) [A >= B && B >= 1 && C >= 2*B && D = B] (?,1) 7. lbl101(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [B >= 1 + D && A >= D && B >= 1 && D >= 1 && C >= B + D] (?,1) 8. lbl101(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [D >= 1 + B && A >= D && B >= 1 && D >= 1 && C >= B + D] (?,1) 9. lbl111(A,B,C,D) -> cut(A,B,C,D) [C >= B && B >= 1 && A >= 2*B && D = B] (?,1) 10. lbl111(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [B >= 1 + D && C >= B && B >= 1 && D >= 1 && A >= B + D] (?,1) 11. lbl111(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [D >= 1 + B && C >= B && B >= 1 && D >= 1 && A >= B + D] (?,1) 12. cut(A,B,C,D) -> stop(A,B,C,D) [A >= B && B >= 1 && C >= B && D = B] (?,1) 13. start0(A,B,C,D) -> start(A,C,C,A) True (1,1) Signature: {(cut,4);(lbl101,4);(lbl111,4);(lbl6,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{},1->{5},2->{12},3->{6,7,8},4->{9,10,11},5->{},6->{12},7->{6,7,8},8->{9,10,11},9->{12},10->{6,7,8} ,11->{9,10,11},12->{},13->{0,1,2,3,4}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D) -> stop(A,B,C,D) [0 >= A && B = C && D = A] (1,1) 1. start(A,B,C,D) -> lbl6(A,B,C,D) [A >= 1 && 0 >= C && B = C && D = A] (1,1) 2. start(A,B,C,D) -> cut(A,B,C,D) [A >= 1 && D = A && B = A && C = A] (1,1) 3. start(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [A >= 1 && C >= 1 + A && B = C && D = A] (1,1) 4. start(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [A >= 1 + C && C >= 1 && B = C && D = A] (1,1) 5. lbl6(A,B,C,D) -> stop(A,B,C,D) [A >= 1 && 0 >= C && D = A && B = C] (1,1) 6. lbl101(A,B,C,D) -> cut(A,B,C,D) [A >= B && B >= 1 && C >= 2*B && D = B] (1,1) 7. lbl101(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [B >= 1 + D && A >= D && B >= 1 && D >= 1 && C >= B + D] (?,1) 8. lbl101(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [D >= 1 + B && A >= D && B >= 1 && D >= 1 && C >= B + D] (?,1) 9. lbl111(A,B,C,D) -> cut(A,B,C,D) [C >= B && B >= 1 && A >= 2*B && D = B] (1,1) 10. lbl111(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [B >= 1 + D && C >= B && B >= 1 && D >= 1 && A >= B + D] (?,1) 11. lbl111(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [D >= 1 + B && C >= B && B >= 1 && D >= 1 && A >= B + D] (?,1) 12. cut(A,B,C,D) -> stop(A,B,C,D) [A >= B && B >= 1 && C >= B && D = B] (1,1) 13. start0(A,B,C,D) -> start(A,C,C,A) True (1,1) Signature: {(cut,4);(lbl101,4);(lbl111,4);(lbl6,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{},1->{5},2->{12},3->{6,7,8},4->{9,10,11},5->{},6->{12},7->{6,7,8},8->{9,10,11},9->{12},10->{6,7,8} ,11->{9,10,11},12->{},13->{0,1,2,3,4}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(cut) = x4 p(lbl101) = x4 p(lbl111) = x4 p(lbl6) = x1 p(start) = x1 p(start0) = x1 p(stop) = x4 Following rules are strictly oriented: [A >= 1 + C && C >= 1 && B = C && D = A] ==> start(A,B,C,D) = A > -1*B + D = lbl111(A,B,C,-1*B + D) [D >= 1 + B && C >= B && B >= 1 && D >= 1 && A >= B + D] ==> lbl111(A,B,C,D) = D > -1*B + D = lbl111(A,B,C,-1*B + D) Following rules are weakly oriented: [0 >= A && B = C && D = A] ==> start(A,B,C,D) = A >= D = stop(A,B,C,D) [A >= 1 && 0 >= C && B = C && D = A] ==> start(A,B,C,D) = A >= A = lbl6(A,B,C,D) [A >= 1 && D = A && B = A && C = A] ==> start(A,B,C,D) = A >= D = cut(A,B,C,D) [A >= 1 && C >= 1 + A && B = C && D = A] ==> start(A,B,C,D) = A >= D = lbl101(A,B + -1*D,C,D) [A >= 1 && 0 >= C && D = A && B = C] ==> lbl6(A,B,C,D) = A >= D = stop(A,B,C,D) [A >= B && B >= 1 && C >= 2*B && D = B] ==> lbl101(A,B,C,D) = D >= D = cut(A,B,C,D) [B >= 1 + D && A >= D && B >= 1 && D >= 1 && C >= B + D] ==> lbl101(A,B,C,D) = D >= D = lbl101(A,B + -1*D,C,D) [D >= 1 + B && A >= D && B >= 1 && D >= 1 && C >= B + D] ==> lbl101(A,B,C,D) = D >= -1*B + D = lbl111(A,B,C,-1*B + D) [C >= B && B >= 1 && A >= 2*B && D = B] ==> lbl111(A,B,C,D) = D >= D = cut(A,B,C,D) [B >= 1 + D && C >= B && B >= 1 && D >= 1 && A >= B + D] ==> lbl111(A,B,C,D) = D >= D = lbl101(A,B + -1*D,C,D) [A >= B && B >= 1 && C >= B && D = B] ==> cut(A,B,C,D) = D >= D = stop(A,B,C,D) True ==> start0(A,B,C,D) = A >= A = start(A,C,C,A) * Step 3: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D) -> stop(A,B,C,D) [0 >= A && B = C && D = A] (1,1) 1. start(A,B,C,D) -> lbl6(A,B,C,D) [A >= 1 && 0 >= C && B = C && D = A] (1,1) 2. start(A,B,C,D) -> cut(A,B,C,D) [A >= 1 && D = A && B = A && C = A] (1,1) 3. start(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [A >= 1 && C >= 1 + A && B = C && D = A] (1,1) 4. start(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [A >= 1 + C && C >= 1 && B = C && D = A] (1,1) 5. lbl6(A,B,C,D) -> stop(A,B,C,D) [A >= 1 && 0 >= C && D = A && B = C] (1,1) 6. lbl101(A,B,C,D) -> cut(A,B,C,D) [A >= B && B >= 1 && C >= 2*B && D = B] (1,1) 7. lbl101(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [B >= 1 + D && A >= D && B >= 1 && D >= 1 && C >= B + D] (?,1) 8. lbl101(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [D >= 1 + B && A >= D && B >= 1 && D >= 1 && C >= B + D] (?,1) 9. lbl111(A,B,C,D) -> cut(A,B,C,D) [C >= B && B >= 1 && A >= 2*B && D = B] (1,1) 10. lbl111(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [B >= 1 + D && C >= B && B >= 1 && D >= 1 && A >= B + D] (?,1) 11. lbl111(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [D >= 1 + B && C >= B && B >= 1 && D >= 1 && A >= B + D] (A,1) 12. cut(A,B,C,D) -> stop(A,B,C,D) [A >= B && B >= 1 && C >= B && D = B] (1,1) 13. start0(A,B,C,D) -> start(A,C,C,A) True (1,1) Signature: {(cut,4);(lbl101,4);(lbl111,4);(lbl6,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{},1->{5},2->{12},3->{6,7,8},4->{9,10,11},5->{},6->{12},7->{6,7,8},8->{9,10,11},9->{12},10->{6,7,8} ,11->{9,10,11},12->{},13->{0,1,2,3,4}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(cut) = x2 p(lbl101) = x2 p(lbl111) = x2 p(lbl6) = x3 p(start) = x2 p(start0) = x3 p(stop) = x2 Following rules are strictly oriented: [A >= 1 && C >= 1 + A && B = C && D = A] ==> start(A,B,C,D) = B > B + -1*D = lbl101(A,B + -1*D,C,D) [B >= 1 + D && C >= B && B >= 1 && D >= 1 && A >= B + D] ==> lbl111(A,B,C,D) = B > B + -1*D = lbl101(A,B + -1*D,C,D) Following rules are weakly oriented: [0 >= A && B = C && D = A] ==> start(A,B,C,D) = B >= B = stop(A,B,C,D) [A >= 1 && 0 >= C && B = C && D = A] ==> start(A,B,C,D) = B >= C = lbl6(A,B,C,D) [A >= 1 && D = A && B = A && C = A] ==> start(A,B,C,D) = B >= B = cut(A,B,C,D) [A >= 1 + C && C >= 1 && B = C && D = A] ==> start(A,B,C,D) = B >= B = lbl111(A,B,C,-1*B + D) [A >= 1 && 0 >= C && D = A && B = C] ==> lbl6(A,B,C,D) = C >= B = stop(A,B,C,D) [A >= B && B >= 1 && C >= 2*B && D = B] ==> lbl101(A,B,C,D) = B >= B = cut(A,B,C,D) [B >= 1 + D && A >= D && B >= 1 && D >= 1 && C >= B + D] ==> lbl101(A,B,C,D) = B >= B + -1*D = lbl101(A,B + -1*D,C,D) [D >= 1 + B && A >= D && B >= 1 && D >= 1 && C >= B + D] ==> lbl101(A,B,C,D) = B >= B = lbl111(A,B,C,-1*B + D) [C >= B && B >= 1 && A >= 2*B && D = B] ==> lbl111(A,B,C,D) = B >= B = cut(A,B,C,D) [D >= 1 + B && C >= B && B >= 1 && D >= 1 && A >= B + D] ==> lbl111(A,B,C,D) = B >= B = lbl111(A,B,C,-1*B + D) [A >= B && B >= 1 && C >= B && D = B] ==> cut(A,B,C,D) = B >= B = stop(A,B,C,D) True ==> start0(A,B,C,D) = C >= C = start(A,C,C,A) * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D) -> stop(A,B,C,D) [0 >= A && B = C && D = A] (1,1) 1. start(A,B,C,D) -> lbl6(A,B,C,D) [A >= 1 && 0 >= C && B = C && D = A] (1,1) 2. start(A,B,C,D) -> cut(A,B,C,D) [A >= 1 && D = A && B = A && C = A] (1,1) 3. start(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [A >= 1 && C >= 1 + A && B = C && D = A] (1,1) 4. start(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [A >= 1 + C && C >= 1 && B = C && D = A] (1,1) 5. lbl6(A,B,C,D) -> stop(A,B,C,D) [A >= 1 && 0 >= C && D = A && B = C] (1,1) 6. lbl101(A,B,C,D) -> cut(A,B,C,D) [A >= B && B >= 1 && C >= 2*B && D = B] (1,1) 7. lbl101(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [B >= 1 + D && A >= D && B >= 1 && D >= 1 && C >= B + D] (?,1) 8. lbl101(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [D >= 1 + B && A >= D && B >= 1 && D >= 1 && C >= B + D] (?,1) 9. lbl111(A,B,C,D) -> cut(A,B,C,D) [C >= B && B >= 1 && A >= 2*B && D = B] (1,1) 10. lbl111(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [B >= 1 + D && C >= B && B >= 1 && D >= 1 && A >= B + D] (C,1) 11. lbl111(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [D >= 1 + B && C >= B && B >= 1 && D >= 1 && A >= B + D] (A,1) 12. cut(A,B,C,D) -> stop(A,B,C,D) [A >= B && B >= 1 && C >= B && D = B] (1,1) 13. start0(A,B,C,D) -> start(A,C,C,A) True (1,1) Signature: {(cut,4);(lbl101,4);(lbl111,4);(lbl6,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{},1->{5},2->{12},3->{6,7,8},4->{9,10,11},5->{},6->{12},7->{6,7,8},8->{9,10,11},9->{12},10->{6,7,8} ,11->{9,10,11},12->{},13->{0,1,2,3,4}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(cut) = -5 + 4*x1 + x2 p(lbl101) = -4 + 4*x1 + x4 p(lbl111) = -5 + 4*x1 + x2 p(lbl6) = 1 + 4*x1 + x4 p(start) = 1 + 4*x1 + x4 p(start0) = 1 + 5*x1 p(stop) = -5 + 4*x1 + x4 Following rules are strictly oriented: [A >= 1 && D = A && B = A && C = A] ==> start(A,B,C,D) = 1 + 4*A + D > -5 + 4*A + B = cut(A,B,C,D) [A >= 1 + C && C >= 1 && B = C && D = A] ==> start(A,B,C,D) = 1 + 4*A + D > -5 + 4*A + B = lbl111(A,B,C,-1*B + D) [A >= B && B >= 1 && C >= 2*B && D = B] ==> lbl101(A,B,C,D) = -4 + 4*A + D > -5 + 4*A + B = cut(A,B,C,D) [D >= 1 + B && A >= D && B >= 1 && D >= 1 && C >= B + D] ==> lbl101(A,B,C,D) = -4 + 4*A + D > -5 + 4*A + B = lbl111(A,B,C,-1*B + D) Following rules are weakly oriented: [0 >= A && B = C && D = A] ==> start(A,B,C,D) = 1 + 4*A + D >= -5 + 4*A + D = stop(A,B,C,D) [A >= 1 && 0 >= C && B = C && D = A] ==> start(A,B,C,D) = 1 + 4*A + D >= 1 + 4*A + D = lbl6(A,B,C,D) [A >= 1 && C >= 1 + A && B = C && D = A] ==> start(A,B,C,D) = 1 + 4*A + D >= -4 + 4*A + D = lbl101(A,B + -1*D,C,D) [A >= 1 && 0 >= C && D = A && B = C] ==> lbl6(A,B,C,D) = 1 + 4*A + D >= -5 + 4*A + D = stop(A,B,C,D) [B >= 1 + D && A >= D && B >= 1 && D >= 1 && C >= B + D] ==> lbl101(A,B,C,D) = -4 + 4*A + D >= -4 + 4*A + D = lbl101(A,B + -1*D,C,D) [C >= B && B >= 1 && A >= 2*B && D = B] ==> lbl111(A,B,C,D) = -5 + 4*A + B >= -5 + 4*A + B = cut(A,B,C,D) [B >= 1 + D && C >= B && B >= 1 && D >= 1 && A >= B + D] ==> lbl111(A,B,C,D) = -5 + 4*A + B >= -4 + 4*A + D = lbl101(A,B + -1*D,C,D) [D >= 1 + B && C >= B && B >= 1 && D >= 1 && A >= B + D] ==> lbl111(A,B,C,D) = -5 + 4*A + B >= -5 + 4*A + B = lbl111(A,B,C,-1*B + D) [A >= B && B >= 1 && C >= B && D = B] ==> cut(A,B,C,D) = -5 + 4*A + B >= -5 + 4*A + D = stop(A,B,C,D) True ==> start0(A,B,C,D) = 1 + 5*A >= 1 + 5*A = start(A,C,C,A) * Step 5: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D) -> stop(A,B,C,D) [0 >= A && B = C && D = A] (1,1) 1. start(A,B,C,D) -> lbl6(A,B,C,D) [A >= 1 && 0 >= C && B = C && D = A] (1,1) 2. start(A,B,C,D) -> cut(A,B,C,D) [A >= 1 && D = A && B = A && C = A] (1,1) 3. start(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [A >= 1 && C >= 1 + A && B = C && D = A] (1,1) 4. start(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [A >= 1 + C && C >= 1 && B = C && D = A] (1,1) 5. lbl6(A,B,C,D) -> stop(A,B,C,D) [A >= 1 && 0 >= C && D = A && B = C] (1,1) 6. lbl101(A,B,C,D) -> cut(A,B,C,D) [A >= B && B >= 1 && C >= 2*B && D = B] (1,1) 7. lbl101(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [B >= 1 + D && A >= D && B >= 1 && D >= 1 && C >= B + D] (?,1) 8. lbl101(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [D >= 1 + B && A >= D && B >= 1 && D >= 1 && C >= B + D] (1 + 5*A,1) 9. lbl111(A,B,C,D) -> cut(A,B,C,D) [C >= B && B >= 1 && A >= 2*B && D = B] (1,1) 10. lbl111(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [B >= 1 + D && C >= B && B >= 1 && D >= 1 && A >= B + D] (C,1) 11. lbl111(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [D >= 1 + B && C >= B && B >= 1 && D >= 1 && A >= B + D] (A,1) 12. cut(A,B,C,D) -> stop(A,B,C,D) [A >= B && B >= 1 && C >= B && D = B] (1,1) 13. start0(A,B,C,D) -> start(A,C,C,A) True (1,1) Signature: {(cut,4);(lbl101,4);(lbl111,4);(lbl6,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{},1->{5},2->{12},3->{6,7,8},4->{9,10,11},5->{},6->{12},7->{6,7,8},8->{9,10,11},9->{12},10->{6,7,8} ,11->{9,10,11},12->{},13->{0,1,2,3,4}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(cut) = x2 p(lbl101) = x2 p(lbl111) = x2 p(lbl6) = x2 p(start) = x2 p(start0) = x3 p(stop) = x2 Following rules are strictly oriented: [A >= 1 && C >= 1 + A && B = C && D = A] ==> start(A,B,C,D) = B > B + -1*D = lbl101(A,B + -1*D,C,D) [B >= 1 + D && A >= D && B >= 1 && D >= 1 && C >= B + D] ==> lbl101(A,B,C,D) = B > B + -1*D = lbl101(A,B + -1*D,C,D) [B >= 1 + D && C >= B && B >= 1 && D >= 1 && A >= B + D] ==> lbl111(A,B,C,D) = B > B + -1*D = lbl101(A,B + -1*D,C,D) Following rules are weakly oriented: [0 >= A && B = C && D = A] ==> start(A,B,C,D) = B >= B = stop(A,B,C,D) [A >= 1 && 0 >= C && B = C && D = A] ==> start(A,B,C,D) = B >= B = lbl6(A,B,C,D) [A >= 1 && D = A && B = A && C = A] ==> start(A,B,C,D) = B >= B = cut(A,B,C,D) [A >= 1 + C && C >= 1 && B = C && D = A] ==> start(A,B,C,D) = B >= B = lbl111(A,B,C,-1*B + D) [A >= 1 && 0 >= C && D = A && B = C] ==> lbl6(A,B,C,D) = B >= B = stop(A,B,C,D) [A >= B && B >= 1 && C >= 2*B && D = B] ==> lbl101(A,B,C,D) = B >= B = cut(A,B,C,D) [D >= 1 + B && A >= D && B >= 1 && D >= 1 && C >= B + D] ==> lbl101(A,B,C,D) = B >= B = lbl111(A,B,C,-1*B + D) [C >= B && B >= 1 && A >= 2*B && D = B] ==> lbl111(A,B,C,D) = B >= B = cut(A,B,C,D) [D >= 1 + B && C >= B && B >= 1 && D >= 1 && A >= B + D] ==> lbl111(A,B,C,D) = B >= B = lbl111(A,B,C,-1*B + D) [A >= B && B >= 1 && C >= B && D = B] ==> cut(A,B,C,D) = B >= B = stop(A,B,C,D) True ==> start0(A,B,C,D) = C >= C = start(A,C,C,A) * Step 6: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D) -> stop(A,B,C,D) [0 >= A && B = C && D = A] (1,1) 1. start(A,B,C,D) -> lbl6(A,B,C,D) [A >= 1 && 0 >= C && B = C && D = A] (1,1) 2. start(A,B,C,D) -> cut(A,B,C,D) [A >= 1 && D = A && B = A && C = A] (1,1) 3. start(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [A >= 1 && C >= 1 + A && B = C && D = A] (1,1) 4. start(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [A >= 1 + C && C >= 1 && B = C && D = A] (1,1) 5. lbl6(A,B,C,D) -> stop(A,B,C,D) [A >= 1 && 0 >= C && D = A && B = C] (1,1) 6. lbl101(A,B,C,D) -> cut(A,B,C,D) [A >= B && B >= 1 && C >= 2*B && D = B] (1,1) 7. lbl101(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [B >= 1 + D && A >= D && B >= 1 && D >= 1 && C >= B + D] (C,1) 8. lbl101(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [D >= 1 + B && A >= D && B >= 1 && D >= 1 && C >= B + D] (1 + 5*A,1) 9. lbl111(A,B,C,D) -> cut(A,B,C,D) [C >= B && B >= 1 && A >= 2*B && D = B] (1,1) 10. lbl111(A,B,C,D) -> lbl101(A,B + -1*D,C,D) [B >= 1 + D && C >= B && B >= 1 && D >= 1 && A >= B + D] (C,1) 11. lbl111(A,B,C,D) -> lbl111(A,B,C,-1*B + D) [D >= 1 + B && C >= B && B >= 1 && D >= 1 && A >= B + D] (A,1) 12. cut(A,B,C,D) -> stop(A,B,C,D) [A >= B && B >= 1 && C >= B && D = B] (1,1) 13. start0(A,B,C,D) -> start(A,C,C,A) True (1,1) Signature: {(cut,4);(lbl101,4);(lbl111,4);(lbl6,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{},1->{5},2->{12},3->{6,7,8},4->{9,10,11},5->{},6->{12},7->{6,7,8},8->{9,10,11},9->{12},10->{6,7,8} ,11->{9,10,11},12->{},13->{0,1,2,3,4}] + Applied Processor: KnowledgePropagation + Details: The problem is already solved. YES(?,O(n^1))